Condensation of Rocky Material in Astrophysical Environments · Ebel: Condensation of Rocky Material in Astrophysical Environments253 253 Condensation of Rocky Material in Astrophysical

Ebel: Condensation of Rocky Material in Astrophysical Environments 253

253

Condensation of Rocky Material inAstrophysical Environments

Denton S. EbelAmerican Museum of Natural History

Volatility-dependent fractionation of the rock-forming elements at high temperatures is anearly, widespread process during formation of the earliest solids in protoplanetary disks. Equi-librium condensation calculations allow prediction of the identities and compositions of min-eral and liquid phases coexisting with gas under presumed bulk chemical, pressure, andtemperature conditions. A graphical survey of such results is presented for systems of solarand nonsolar bulk composition. Chemical equilibrium was approached to varying degrees inthe local regions where meteoritic chondrules, Ca-Al-rich inclusions, matrix, and other com-ponents formed. Early, repeated vapor-solid cycling and homogenization, followed by hierar-chical accretion in dust-rich regions, is hypothesized for meteoritic inclusions. Disequilibriumchemical effects appear to have been common at all temperatures, but increasingly so in less-refractory meteoritic components. Work is needed to better model high-temperature solid solu-tions, indicators of these processes.

1. INTRODUCTION

It may be that much of the early solar nebula consistedof completely vaporized primordial material (>1800 K) thatcooled monotonically (Cameron, 1963; Kurat, 1988). Thisscenario explains the astonishing isotopic homogeneity (ex-cept O) of solar system materials from interplanetary dustgrains (IDPs), to chondrites, to planets (e.g., Zhu et al.,2001), but it appears to violate current theories about thethermal structure of the nebula and protoplanetary disk(Cameron, 1995; Gail, 1998; Woolum and Cassen, 1999).Yet equilibrium condensation sequences capture many first-order observations of the volatility-dependent fractionationsof the elements, the identities of their host phases in mete-orites, and even the chemical structure of the solar system(Humayun and Cassen, 2000). In the first edition of this vol-ume, MacPherson et al. (1988) concluded that “ . . . goodchemical and sparse textural evidence indicate that vapor-solid condensation played a major role in the genesis ofmany refractory inclusions in the early solar nebula. Thecondensation probably reflected neither perfect equilibriumnor perfect fractionation.” Volatility-related fractionationsamong rocky elements were established at high tempera-tures, and are recorded in CAIs and chondrules (Grossman,1996). The focus here is the vapor-liquid-solid equilibriarelevant to these fractionation processes.

As investigations focus on disk structure, descriptions ofchemical equilibrium between gas + silicate liquid + solidphases constrain the likelihood and extent of local processesthat might occur in dense, cool disk regions subject to gravi-tational instabilities and shock heating (e.g., Wood, 1996;Iida et al., 2001; Desch and Connolly, 2002; Ciesla andHood, 2002); in hotter, partially ionized regions subject tomagnetorotational turbulence and current sheet heating (e.g.,

Joung et al., 2004); or in streams of material subject to solarflares and winds [the x-wind of Shu et al. (2001)]. Param-eterizations of chemical equilibrium calculations can be in-tegrated into large-scale nebula models (e.g., Cassen, 2001).Condensation calculations are also applicable to other astro-physical environments, such as the stellar atmospheres thatproduce refractory interstellar dust (Lattimer et al., 1978;Lodders and Fegley, 1997; Ebel, 2000). With new analyti-cal techniques, meteoriticists have sharpened the search forpristine solar nebula condensates and their isotopic andtrace-element signatures, but also recognized that factorsother than their thermal stability in a cooling gas have af-fected the chemistry of the most primitive objects found inmeteorites.

The cosmochemical classification of the elements is basedon their relative volatilities in a system of solar bulk com-position. In a cooling (or heating) solar gas, elements arecalculated to condense (or evaporate) in groups dependentupon their volatility: the abundant elements Ca, Al, and Tiare highly refractory; Si, Mg, and Fe are less refractory; Kand Na are moderately volatile; S and C are more volatile.The rare earth (REE), platinum group (PGE), and other traceelements (e.g., highly volatile Hg, Tl) can be similarly clas-sified (e.g., Kerridge and Matthews, 1988, Part 7; Irelandand Fegley, 2000). These groups may be correlated, or com-bined, with Goldschmidt’s (1954) geochemical classifica-tion of lithophile, siderophile, chalcophile, and atmophileelements (Larimer, 1988; Hutchison, 2004). The chemicalcompositions and associations of the most ancient mineralsin meteorites strongly suggest that their formation was con-trolled in large part by the relative volatilities of the oxidesof their constituent elements. Observed fractionations ofthe elements between meteoritic (asteroidal), cometary, andplanetary reservoirs are also correlated to volatility (Lewis,

254 Meteorites and the Early Solar System II

1972a,b). We model high-temperature equilibrium and dis-equilibrium processes to understand the formation of me-teorite components, and the fractionation of the elements,one from another, in our solar system and in other stellarenvironments.

1.1. Chemical Equilibrium Calculations

“Condensation calculation” is a generic term for mod-els describing the equilibrium distribution of the elementsbetween coexisting phases (solids, liquid, vapor) in a closedchemical system with vapor always present. Predictions ofchemical equilibrium made using the equations of state ofthe phases involved, for example, at fixed total pressure(Ptot) and temperature (T), are independent of whether or notthe system is cooling. They do not predict the sizes of resul-tant crystals. They can, however, be used to characterize thedegree to which a chemical system is supersaturated in a po-tential condensate, which is a key parameter in understand-ing nucleation of condensates. Condensation calculationshave been performed to describe chemistry in astrophysi-cal environments since before digital computers becamecommonplace (Latimer, 1950; Urey, 1952; Lord,1965; cf.historical review by Lodders and Fegley, 1997). Lodders(2003) has most recently computed the condensation tem-peratures of all the elements into pure, stoichiometric solidminerals from a cooling vapor of solar composition at Ptot =10–4 bar. Others have recently explored the stability of con-densed liquid oxide solutions as well as solid solutions, allcoexisting with vapor, in systems enriched in previously va-porized chondritic dust (e.g., Yoneda and Grossman, 1995;Ebel and Grossman, 2000). Chemical equilibrium calcula-tions describe the identity and chemical composition of eachchemical phase in the assemblage toward which a givenclosed system of elements will evolve, to minimize thechemical potential energy of the entire system. This knowl-edge is a prerequisite to any discussion of whether, where,how, and why equilibrium was or was not achieved in anyparticular scenario predicted by astrophysical models, or inrelation to the origin of any particular meteoritic object.

Equilibrium calculations strictly apply only to systemsthat can be assumed to have reached or closely approachedchemical equilibrium at a given point in their history. Dis-equilibrium effects can be explored by modification ofequilibrium calculations, for example, fractionation or diffu-sion, by removing high-T condensates from further reac-tion at lower T (Larimer, 1967; Larimer and Anders, 1967;Petaev and Wood, 1998a,b, 2000; Meibom et al., 2001);retarded nucleation, by constraining the onset of conden-sation for particular phases (Blander et al., 2005; but cf.Stolper and Paque, 1986); evaporation, by computing satu-ration vapor pressures over evaporating phases, for inputinto kinetic models (e.g., Grossman et al., 2000; Nagaharaand Ozawa, 2000; Alexander, 2001; Richter et al., 2002); orphotodissociation of gaseous molecules, by adjusting theirthermal stabilities (Ebel and Grossman, 2001).

Reaction network calculations are a very different kindof simulation, in which the rates of individual reactions

are addressed explicitly through rate constants. Parameters(e.g., reaction rates, sticking coefficients, surface energiesof small clusters, and heterogeneous catalytic effects of dustgrains) for full gas-dynamical treatments (e.g., Draine, 1979;Chigai et al., 2002) of heterogeneous reactions among rock-forming elements at high temperature are very poorly con-strained. Network calculations appear to be most effectivefor low-temperature phase relations, and gas-phase reactionsin the H-C-N-O-S system (e.g., Hasegawa and Herbst, 1993;Bettens and Herbst, 1995; Gail, 1998; Aikawa et al., 2003;Semenov et al., 2004). Partial ionization of gas would cer-tainly affect condensation, and photodissociation would alsooccur in regions subject to ionizing radiation. Thermal ion-ization is not significant at the conditions discussed here,and calculations to the present do not address the conden-sation of rocky material in astrophysical environments withsignificant flux of ionizing radiation.

The formalism of classical thermodynamics is rootedin the phenomenology of materials, calibrated against morethan a century of laboratory investigation (e.g., Bowen, 1928;Nurse and Stutterheim, 1950; Newton, 1987; Ganguly,2001). Powers of interpolation, extrapolation, and predic-tion stem from this formalism (cf., DeHeer, 1986; Ander-son and Crerar, 1993). This tool, and detailed observationsof meteoritic inclusion and matrix chemistries and textures,constrain the conditions and processes these rocky materi-als might have experienced. Hypotheses for their formationmust predict chemical, thermal, and mechanical conditionsthat are in accord with those constraints. Pressures, tempera-tures, oxygen fugacities, and chemical environments are de-duced from analyses of meteoritic materials, and constrainastrophysical models for the protoplanetary disk in whichthose materials formed. The resulting understanding of theuniversal process of disk formation is central to learninghow and where habitable planets form, and how unique ourown Earth really is.

1.2. Earlier Reviews and Present Focus

Several excellent reviews cover condensation of crys-talline solid phases from a gas of solar composition (e.g.,Larimer, 1988; Lewis, 1997; Fegley, 1999), particularlyGrossman and Larimer (1974). Davis (2003) has comparedkinetically controlled processes with equilibrium processes.The present chapter briefly describes data and algorithmsfor modeling the thermal stability of condensates relativeto vapors of various compositions, presenting results in theform of phase diagrams with a discussion of their use. I alsobriefly discuss the meteoritic evidence that may indicatedirect condensation, or the establishment of chemical equi-librium between gas, solid, and liquid phases in the proto-planetary disk before accretion of the meteorite parentbodies.

Dust-gas chemistry has received substantial attentionfrom astrophysicists interested in interstellar and cometarymaterial (e.g., Millar and Williams, 1993; Altwegg et al.,1999). The role of interstellar processes in establishing themeteorite record is increasingly recognized (e.g., Wood,


1998; Irvine et al., 2000). Some grains found in meteoriteswere formed at high temperatures around stars with C/O ≥1, or in supernovae (cf. Zinner, 1998; Nittler and Dauphas,2006). Astrophysical observations (e.g., Chen et al., 2003)are yielding new data about stars of nonsolar metallicity(i.e., the abundance of H relative to all the heavier elements;in astrophysics, metals — here, metal will refer to Fe, Ni,Co, etc., and their alloys). Measurement of the atmosphericcompositions of stellar grain sources is an active field, asis modeling of nucleosynthesis in AGB stars and novae.Condensation calculations using these results as inputs arevital to understanding the origins of interstellar and presolargrains (e.g., Amari et al., 2001; Ebel and Grossman, 2001;cf. review by Lodders and Fegley, 1997). Grain formationin stellar outflows is also central to understanding the vola-tility-dependent depletions of rock-forming elements ob-served in the interstellar medium (Field, 1974; Irvine et al.,1987; Ebel, 2000; Kemper, 2002). Condensation calcula-tions have been pursued down to absolute zero (Lewis,1972a); however, the equilibrium model is of very limitedutility at such low temperatures. High-temperature disequi-librium effects, such as temperature differences between gasand solids (e.g., Arrhenius and Alfvén, 1971), can be ad-dressed by modification of equilibrium calculations. Thischapter is about the fates of condensable atoms in the nebulaand disk, at temperatures above 1000 K, and total pressuresbetween 10–8 and 1.0 bar (number densities of molecules>3 × 1016 cm–1). These are conditions, plausible in some butnot in all astrophysical models of portions of the protoplane-tary disk, where ensembles of atoms may be assumed to ap-proach chemical equilibrium on timescales that make suchcalculations relevant and useful.

2. TECHNIQUES

2.1. Elemental Abundances

2.1.1. Solar and carbon-enriched systems. The calcu-lations here consider closed chemical systems containingthe 22 elements having abundance greater than Zn, plus F:H, He, C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K, Ca,Ti, Cr, Mn, Fe, Co, Ni. Equilibrium among these elementsfixes their partial pressures in the vapors, from which ther-mal stabilities of trace-element-bearing compounds can becalculated. The relative atomic fractions of the elements ina vapor of solar composition are from Anders and Grevesse(1989), which give a C/O ratio of 0.43. Recent work byAllende Prieto et al. (2002) resets solar C/O to 0.50, andLodders (2003) has most recently reevaluated solar abun-dances of all the elements (cf. Grevesse and Sauval, 2000).These revisions have very minor effects on the relative ther-mal stabilities of rocky condensates. Because C and O com-bine to form the highly stable CO gaseous molecule, theexcess O makes a gas of solar composition oxidizing. If C/O > ~1.0 by addition of C to, or removal of H2O from, a gasof otherwise solar composition, the system becomes highlyreducing, and very different solid assemblages become sta-ble. Carbon-enriched gas compositions are relevant to the

formation of presolar graphite, SiC, TiC, and other grainsin C-rich stellar environments (Sharp and Wasserburg, 1995;Lodders and Fegley, 1997), and possibly also to the forma-tion of enstatite chondrites (Ebel and Alexander, 2005).

2.1.2. Dust-enriched systems. Innumerable scenarioscan be explored for adjusting elemental abundances in a gasof solar composition, by the addition or subtraction of plau-sibly fractionated components. Wood (1963, 1967) proposedenrichment of vapor of solar composition by a fractionateddust of previously condensed rocky material, perhaps in themidplane of a protoplanetary disk to as far as 10 AU (Millaret al., 2003). In this scenario, dust consisting of oxides andsulfides of rock-forming elements is concentrated relativeto H2 and other volatile species. The resulting bulk com-position is assumed to be heated to vaporization, and thecondensation history of the cooling vapor is predicted. Woodand Hashimoto (1993) explored the condensation of bulkcompositions enriched or depleted in refractory, organic,and icy components and in H. Yoneda and Grossman (1995)explored condensation in solar bulk compositions enrichedby a dust of ordinary chondrite composition. Their objec-tive was to find the conditions where CaO-MgO-Al2O3-SiO2(CMAS) liquids are stable. Ebel and Grossman (2000) ex-tended this work to a vapor of solar composition, enrichedin a dust of carbonaceous chondrite (Orgueil, CI) compo-sition, and they calculated the thermal stability of CMAS-TiO2-FeO-Na2O-K2O liquids and FeO-bearing silicates. Theportion of a vapor of solar composition that Ebel and Gross-man (2000) considered to be condensable as chondritic (CI)dust is 5.66 × 10–4 (atomic), or 6.69 × 10–3 (by mass), of acanonical solar vapor (Anders and Grevesse, 1989). Theirdust enrichment factor of 1000× CI corresponds to a dust/gas mass ratio of ~6.7, which is not unjustifiable on astro-physical grounds. Chondritic material is highly depleted inC and H relative to solar. The addition of such “dust” to agas of solar composition increases the partial pressure ofO in particular, but also condensable elements present inthe dust.

2.2. Thermodynamic Data

If everyone used the same data and algorithms, therewould be a unique canonical “condensation sequence.” Suchis not the case, and in recent years differences have beenexaggerated by the employment of ever more complexmodels for mineral solid solutions: minerals where multiplecombinations of elements can occupy sites in the same crys-talline lattice. There is no single “most correct” database,or set of solid-solution models; however, there are carefullyselected, internally consistent sets of data, and haphazardlyselected sets collected from disparate sources. The formershould be more correct, in application, than the latter. Thepower and limitations of a particular calculation are mostclear when algorithms, but most importantly the core data,are described as completely as editors will allow. For ex-ample, the mixing of endmember olivine species fayalite(Fe2SiO4) and forsterite (Mg2SiO4) can be treated as a me-chanical mixture of separately condensing endmembers, or


as a real solid solution with accounting (based on experi-mental data) for the energetic consequences of ionic mixingon the olivine crystalline lattice. The particulars of data, andhow it is implemented in calculation, are crucial to evalu-ating the results of such calculations.

There is reasonable agreement as to the first-order phe-nomena predicted during equilibrium cooling of a gas ofsolar composition at fixed Ptot (Larimer, 1967; Grossman,1972; Grossman and Larimer, 1974; Wood and Hashimoto,1993; Yoneda and Grossman, 1995; Ebel and Grossman,2000; Lodders, 2003) (see section 3.1.2). Calculations ofsilicate liquid stability as a function of Ptot and enrichmentin chondritic dust also agree where models overlap (Yonedaand Grossman, 1995; Ebel and Grossman, 2000; Ebel,2005).

An important consideration is the fundamental thermo-dynamic data for the elements, depending upon what formsof equations of state are used for solids and liquids. Theequations of state for compounds used here combine theirenthalpy and entropy of formation from the elements intheir standard states at 298 K and 1 bar with the heat ca-pacity of the compound at all relevant temperatures. Fromthese data, suitable equations of state (e.g., apparent Gibbsenergy of formation from the elements at constant P andT) are readily calculated from free-energy (Giaque) func-tions for the constituent elements (cf. Ghiorso and Kelemen,1987; Berman, 1988; Anderson and Crerar, 1993). Directuse of tabulated Gibbs energies (e.g., Chase, 1998) can behazardous (cf. Lodders, 2004).

2.2.1. Major elements. Equilibria between gas, solid,and liquid phases are most conveniently calculated by refer-ring all formation reaction energies to the monatomic gas-eous species of the elements. The elements can be dividedinto major, minor, and trace categories based upon their ab-solute abundances. The abundant elements are atmophile(gaseous) H, C, N, O; lithophile (“rock-loving”) Si, Mg, Al,Ca, Ni, Na, K, Ti; and siderophile (“iron-loving”) Fe, Ni, Co,Cr, and S. Just the oxides of Si and Mg, with metallic Fe,constitute >85% of matter condensable above 400 K from avapor of solar composition. Most of the other elements haveminor effects on the identity and compositions of solids andliquids into which they substitute in equilibrium with vaporunder most assumed astrophysical conditions.

2.2.2. Minor and trace elements. These elements usu-ally occur as trace substituents in minerals, so they are fre-quently considered separately from the major, or abundant,rock-forming elements that make up those minerals. Therare earth elements (REE), U, Th, Li, and others are litho-phile; siderophile trace elements include the platinum groupelements (PGE) (Ru, Rh, Pd, Re, Os, Ir, Pt). The moderatelyvolatile elements (e.g., Mn, Cu, Na, Se, Zn, Cd) were de-fined by Larimer (1988) as “never depleted by more than afactor of 5 in any chondrite, relative to CI,” and displaying“no detectable variations within a chondrite group” (cf. Xiaoand Lipschutz, 1992). Hutchison (2004) delineates the 50%condensation T of Cr as separating refractory from moder-ately volatile (Au, Mn, alkalies) elements, and the onset of

FeS condensation as marking the T below which “highlyvolatile” elements (Pb, Tl, Bi, Cd, Hg, In) condense. In mostcalculations, these trace elements are allowed to condenseas pure elemental, oxide, or sulfide solids, which are thenassumed to dissolve into major-element phases present atcorresponding conditions. For example, most Cd condensesas CdS, at temperatures where FeS is stable (e.g., Lodders,2003), hence CdS is assumed to dissolve into FeS. Equa-tions of state for the gaseous and solid oxides and othercompounds of many minor elements are poorly known ornot readily available (Davis and Grossman, 1979). The rela-tive solubilities of these elements between gas, solid, andliquid phases are in most cases also not well understood,so analysis of meteoritic minerals usually guides the choiceof host phase. Thus in “oxidized” systems (e.g., solar), theREE condense into perovskite or hibonite (Lodders, 2003),and in reduced systems into oldhamite [Lodders and Fegley(1993) and formulae in Table 1], based on measurementsof those phases in ordinary and enstatite chondrites (e.g.,Crozaz and Lundberg, 1995), and on the condensation tem-peratures of pure REE oxides and sulfides. The refractorysiderophile elements including PGE are expected to con-dense into refractory metal nuggets at high temperatures (ElGoresy et al., 1979; Fegley and Palme, 1985; Lodders, 2003;Campbell et al., 2001), and into Fe-Ni alloy when Fe con-denses. The behavior of trace elements becomes less pre-dictable as their volatility increases, because the assumptionof equilibrium becomes less tenable at lower T (Kornackiand Fegley, 1986).

2.2.3. Gaseous species. The primary reservoir of thenebula and disk is a vapor containing hundreds of gaseousmolecular species (e.g., H, C, O, H2, CO, CO2, H2O). Atand below Ptot = 1 bar the gas can be considered as an idealmixture of ideal gases. Because most gas species data is de-rived from vibrational spectroscopic measurements (Chase,1998), it is assumed to be internally consistent. That is, anequilibrium calculation using data for reacting species ac-curately reproduces equilibria involving those species as ob-served in the laboratory. Algorithms to minimize the chemi-cal potential energy in a large, speciated gaseous systemstem from the work of White et al. (1958) (cf. Smith andMissen, 1982).

2.2.4. Pure solid species. Of the 275 mineral speciesidentified in meteorites (Rubin, 1997), only a small subsetis abundant, stable at high T, and has well-known thermo-dynamic properties. Much of the high-quality data for solidphases of geologic interest was determined many years ago,in labor-intensive systematic investigations by dedicated ex-perimentalists. Mineral phases common in terrestrial geol-ogy are well studied; however, data are absent for somehigh-temperature phases found in chondrites [e.g., rhönite(Fuchs, 1978; see Beckett et al., 2006)]. Data used in cal-culations must account for phase transitions that occur inmany solids (e.g., α-β quartz–cristobalite for SiO2), as theirmost stable crystalline lattice structure changes with tem-perature. Most magnetic transitions are below the tempera-tures at which equilibrium calculations might be assumed


to apply, and they are not considered here. Multiple datacompilations and laboratory studies contain equations ofstate for mineral phases of interest (cf. Berman, 1988; Kuz-menko et al., 1997). For example, for six published valuesfor the enthalpy of formation of grossite from the elementsat 298 K, the average is –4012.261 kJ, with a standard de-viation of 11.413 kJ (Berman, 1983; Geiger et al., 1988,and references therein). A similar selection exists for hibon-ite (Kumar and Kay, 1985) and perovskite (formulae inTable 1). These differences affect the stabilities of Ca-alu-minates relative to competing oxides, and account for manydifferences in published condensation sequences (see sec-tion 3.1.2), as reviewed in detail by Ebel and Grossman(2000). In nature, Mg and Ti dissolve into hibonite (Hintonet al., 1988; Beckett and Stolper, 1994; Simon et al., 1997;Beckett et al., 2006), and this behavior is not captured inany calculations to date. Treating these phases as solid solu-tions is a goal of future work. Various permutations of allavailable data allow a variety of predictions for the relativestabilities of endmember (pure) corundum, hibonite, Ca-aluminate, grossite, spinel, and perovskite (Table 1) with-out appreciably altering the relative proportions of Ca, Al,and Ti oxides that are condensed at a particular T and Ptot.This is because the differences in the free energies for thesolid phases are small, compared to the differences in freeenergies of the solids relative to the vapor.

2.2.5. Solid solutions. Many minerals found in mete-orites, and predicted to be thermodynamically stable at hightemperatures in a gas of solar composition, are solutionsof two or more endmember components with the same crys-tal structure. Because these solid-solution minerals incor-porate variable amounts of several elements depending uponthe conditions in which they form, they are potentially pow-erful indicator minerals for constraining the condensation,evaporation, and crystallization histories of meteoritic in-clusions in which they occur (e.g., Fraser and Rammensee,1982). Examples include

melilite: Ca2Al2SiO7 – Ca2MgSi2O7 gehlenite – åkermanitesubstitution: Al2 for MgSi

olivine: Mg2SiO4 – CaMgSiO4 – Fe2SiO4forsterite – monticellite – fayalitesubstitution: Fe and Ca for Mg

metal alloy: Fe,Cr,Co,Si,Ni(note: C, P, S not considered here)

Melilite is a binary solid solution, exhibiting complete solidsolution between the endmembers gehlenite and åkermanite.It is a charge-coupled substitution, since two Al3+ are re-placed by the Mg2+–Si4+ pair. Magnesium-olivine has lim-ited substitution of Ca, but complete substitution of Fe.Efforts to account for such crystal-chemical effects in equa-tions of state comprise a very large geological, metallurgi-cal, and materials science literature, both experimental and

theoretical (Geiger, 2001). For example, existing models arenot capable of accurately predicting the crystallization ofmelilite from silicate liquid (L. Grossman et al., 2002, theirFig. 1), therefore they are also unlikely to model gas-melil-ite equilibria correctly. Yet there is no guarantee that tweak-ing the model for melilite thermodynamics to work with aparticular liquid model will improve the situation. Consis-tency of calibration across all the models used in a calcula-tion is a goal of future work.

The most successful efforts at modeling groups of pureendmember minerals (e.g., Berman, 1988), mineral solidsolutions (e.g., Sack and Ghiorso, 1989), or complex geo-chemical systems such as crystallizing magmas (e.g., Ber-man, 1983; Ghiorso and Sack, 1995), are based on simul-taneous optimization of equations of state that describemultiple experimentally determined equilibrium phase re-lations. Results of these efforts to describe terrestrial rocksare called “internally consistent,” because each piece of datais evaluated and weighted in the context of the entire data-set to optimize agreement with measurements. Less data isavailable to describe less-common substitutional elements(e.g., Cr, Mn, Ni in olivines and pyroxenes) that may bemore important in extraterrestrial rocks.

The most complex solid solution important to the con-densation of rocky material at high T is Ca-rich pyroxene.A comprehensive formulation of a thermodynamic modelof pyroxenes with the general formula

(Ca, Mg, Fe2+, Ti4+, Fe3+, Al)2 (Si, Al, Fe3+)2 O6

is by Sack and Ghiorso (1989, 1994), who concentratedtheir calibration range on the pyroxene compositions com-mon to basaltic igneous rocks. In particular, their Ti-,Al-pyroxene properties were constrained mainly by studies ofbasaltic FeO-bearing systems (Sack and Carmichael, 1984).Their model reproduces many of the chemical characteris-tics of experimental and natural pyroxene-bearing mineralassemblages, but not the Ti3+-bearing pyroxenes (formerlyknown as fassaite) found in CAIs. Beckett (1986) identi-fied four endmembers critical to describing pyroxenes inCAIs — diopside = CaMgSi2O6, CaTs = CaAl2SiO6–, T3P =CaTi3+AlSiO6, and T4P = CaTi4+Al2O6 — estimated Gibbsfree energies for the Ti species; and provided a robustmethod for calculating these component molecular fractionsfrom oxide weight percent data. Although it includes theTi3+ substitution, the model used by Yoneda and Grossman(1995) ignores Fe, and is not calibrated against models ofother solid solutions, or against liquids.

A thermodynamic activity model for solid metal alloywas developed by Grossman et al. (1979) and revised byEbel and Grossman (2000). Although treatments of morecomplex systems are reported in the metallurgical literature(e.g., Fernández-Guillermet, 1988), they have not yet beenincorporated into published condensation calculations. Im-plementations used in industry are proprietary (e.g., Eriks-son, 1975; Eriksson and Hack, 1990; Bale et al., 2002; seealso http://www.esm-software.com/chemsage/). Other work-


ers have treated specific metal subsystems (e.g., Wai andWasson, 1979; Fegley and Palme, 1985). Kelly and Larimer(1977) used thermodynamic theory to trace the history ofsiderophiles from condensation through planetary differen-tiation; however, the effects of C, S, and P were not con-sidered. Petaev et al. (2003) have coupled a model for dif-fusion in metal (Wood, 1967) with condensation chemistryto address the formation of zoned metal grains (Meibom etal., 2001). The results described here do not include anyassumptions about grain sizes or residence times, nor is dif-fusion data considered strong enough to warrant modelingdiffusion in large-scale dust-gas systems.

In reduced chemical systems with high C/O ratios, car-bide, nitride, and sulfide minerals are calculated to be stable,and also intermetallic compounds (e.g., FeSi). We do notyet know how to model many reduced solid solutions. Forexample, a wide range of niningerite (Fe, Mg, Mn)S com-positions is found in meteorites (Ehlers and El Goresy,1988), yet this solid solution is not accounted for in existingequilibrium stability calculations for highly reducing sys-tems (e.g., Lodders and Fegley, 1997). This is a fertile areafor future work.

2.2.6. Liquid solutions. Two well-tested models existfor describing the thermodynamic activities of oxide com-ponents in silicate liquids, suitable for modeling crystal-liq-uid equilibria in magmatic systems. Igneous CAIs and chon-drules are subsets of the universe of such systems. Bothmodels use a classical nonideal thermodynamic formalism(cf. Anderson and Crerar, 1993) to describe the chemicalpotential energy of silicate liquids, and are calibrated againstinternally consistent datasets describing coexisting mineralphases (but not metal alloy). Berman’s (1983) model is re-stricted to CaO-MgO-Al2O3-SiO2 (CMAS) liquids. Ghiorsoand Sack’s (1995) “MELTS” model includes additionalcomponents containing the oxides TiO2, FeO, Cr2O3, P2O5,Na2O, and K2O, but because of their choice of stoichiomet-ric endmember components, it requires that liquids havemolar SiO2 > [½ (MgO-Cr2O3) + ½ FeO + (CaO-3 P2O5) +Na2O + ½ K2O]. In the absence of a tested, universal liq-uid model, one must use either one model or the other, de-pending upon the composition region of interest (cf. Ebeland Grossman, 2000; Ebel, 2005). Berman’s (1983) modelcan be applied to CAIs and FeO-poor chondrules, while theMELTS model applies to most chondrule compositions. Thelimit on MELTS liquid compositions is particularly restric-tive in considering FeO evaporation (Ebel, 2005).

To calibrate the thermodynamic parameters of a modelliquid requires multiple statements of crystal-liquid equi-libria at known P and T derived from laboratory data, com-bined with accurate thermodynamic models of the cryst-alline phases involved (Ghiorso, 1985, 1994; Berman andBrown, 1987). The Berman (1983) CMAS model is cali-brated using an optimized endmember mineral thermody-namic dataset (Berman, 1983), but all solid solutions aretreated as mechanical mixtures of endmembers (e.g., L.Grossman et al., 2002, their Fig. 1). The MELTS model(Ghiorso and Sack, 1995) is calibrated using an internallyconsistent endmember dataset for solid mineral endmem-

bers (Berman, 1988), and complex, nonideal solid-solutionmodels for olivine (Sack and Ghiorso, 1989), pyroxene (Sackand Ghiorso, 1994), feldspar (Elkins and Grove, 1990), spi-nel (Sack and Ghiorso, 1991a,b), etc. These models includeenergetic effects of atomic order/disorder in crystalline lat-tices, but not magnetic effects that may contribute below~800 K. In calculations involving solid solutions and liq-uids, there are many choices to be made; none is perfect.

2.3. Algorithms

2.3.1. Gas-solid-liquid equilibria. In all the calcula-tions considered here, the gas is considered as the primaryreservoir of material. Two approaches may be taken. First,the entire system can be solved as a whole, which amountsto treating each pure solid species as if it were a gaseousmolecule, but with a very different equation of state. Yonedaand Grossman (1995) were the first to incorporate truesolid-solution behavior into such an approach. Alternatively,Ebel and Grossman (2000) solved speciation in the gasseparately (cf. White et al., 1958; Grossman and Larimer,1974; Lattimer et al., 1978; Smith and Missen, 1982; Lewis,1997), treating the gas as a separate solution phase similarto pyroxene or liquid. These approaches yield identical re-sults for the same inputs. Ebel and Grossman (2000) adaptedalgorithms of Ghiorso (1985, 1994) to facilitate use of thesolid- and liquid-solution models embodied in the MELTScode (Ghiorso and Sack, 1995). They substituted gas forliquid as the material reservoir in the MELTS algorithm, andtreated liquids analogously to solid-solution phases.

2.3.2. Solid stability and optimization. This is the mostlaborious part of condensation calculations, particularlywhen a rigorous treatment of solid solutions is included. Thegoal is to find the optimal distribution of elements betweengas and all possible condensates, with no a priori knowl-edge of what the stable condensates are. At any step in aparticular calculation, the thermodynamic stability of allpotential condensates can be calculated from their equationsof state, given the partial pressures of their constituent ele-ments in the gas. Each stable condensate must be added tothe system in a small mass increment, with complementarysubtraction of mass from the gas. Minimization of the chem-ical potential energy (e.g., Gibbs energy) of the gas + con-densate system follows, by redistribution of matter betweenall the coexisting phases. Thermodynamic stability of po-tential condensates is then tested again. Condensates whosemass decreases below a threshold are returned to the gasreservoir (cf. Ebel et al., 2000), where their component ele-ments are removed into more stable condensates in subse-quent steps.

3. RESULTS

Results are presented here in terms of total pressure (Ptot,bar) and temperature (T, in Kelvin) (e.g., Plate 7). Abbre-viations and chemical formulae used in Plate 7 and else-where are listed in Table 1. Discussion logically follows thebehavior of cooling systems of particular bulk composition


at fixed Ptot, following descending vertical paths. It mustbe emphasized that temperature is only one state variableaffecting stable phases; pressure is just as important, as isthe bulk vapor composition. Boundaries mark the conditionsat which particular condensed phases either appear (becomestable), or disappear along such cooling paths. Stable min-eral assemblages, in phase fields, are listed from most- toleast-refractory phase where space permits (e.g., Plate 7).In all cases, vapor is present, and it should be rememberedthat at most temperatures shown, major elements are con-tinually condensing from gas into solid and/or liquid phaseswith cooling: The condensate assemblage, alone, does notrepresent a closed system at any point in any diagram.

Although models for solid solutions (Table 1) containmany potential compositions, less-refractory endmembersare not commonly stable in the systems investigated here.Feldspar is nearly always pure anorthite CaAl2Si2O8, oli-vine pure forsterite Mg2SiO4 with minor Ca. Melilite andCa-pyroxene show the greatest variation in composition athigh temperatures (cf. Ebel and Grossman, 2000).

3.1. Equilibria in a Gas of Solar Composition

3.1.1. Effect of pressure. Plate 7 illustrates equilibriumstability relations of vapor, solid, and liquid phases calcu-lated by this author, with 10–8 < Ptot < 1 bar, and 1100 < T <2000 K, in a closed system of solar composition (Anders

and Grevesse, 1989). The method and data are those re-ported in Ebel and Grossman (2000), who found that therefractory minerals cordierite and sapphirine should becomestable by reaction with other solids at T and Ptot below thetemperature at which virtually all Mg, Al, Si, and Ca arecondensed. Cordierite and sapphirine are extremely rare inmeteorites (Sheng et al., 1991; Rubin, 1997), they are calcu-lated to be stable only at relatively low temperatures, and as-semblages bearing them are only stable, relative to those re-ported here, by order <10–2 J (e.g., at Ptot = 10–4, 8 × 10–4 Jat 1300 K, 3 × 10–3 at 1200 K) relative to other solids (i.e.,well within error); they have been omitted from all the cal-culations reported here. Although Na-,Fe-free cordierite iscalculated to be near the minimum free-energy configura-tion, the cordierite found by Fuchs (1969) has 3–6 wt%Na2O. The absence of cordierite in meteorites suggests theimportance of mineral reconstructive kinetics even at tem-peratures near the stability field of feldspar.

Plate 8 shows a subportion of Plate 7, illustrating phaserelations involving feldspar at low Ptot. Phase boundariesare marked “in”/“out” to signify phase appearance/disap-pearance upon cooling at constant Ptot. A common occur-rence in this and other results (e.g., liquid field in Plate 7) isthe stability of a particular phase over two different T rangesat a fixed Ptot. This results from the continued condensa-tion of major elements (e.g., Si) upon cooling (cf., Yonedaand Grossman, 1995, liquid field in their Fig. 5). The con-

TABLE 1. Names, abbreviations, and chemical formulae of mineral phases.

Mineral Abbreviation Chemical Formula

corundum cor Al2O3

hibonite hib CaAl12O19

grossite grs CaAl4O7Ca-monoaluminate CA1 CaAl2O4perovskite prv CaTiO3melilite mel Ca2(Al2, MgSi)SiO7Al-spinel Al-spn Al-rich (Fe,Mg,Cr,Al,Ti)3O4

Cr-spinel Cr-spn Cr-rich (Fe,Mg,Cr,Al,Ti)3O4

olivine olv (Mg2, Fe2, MgCa)SiO4metal alloy met Fe,Ni,Co,Cr,Sifeldspar fsp (CaAl, NaSi, KSi)AlSi2O8Ca-pyroxene Ca-px Ca(Mg,Fe,Ti4+,Al,Si)3O6orthopyroxene opx MgSiO3-FeSiO3

rhombohedral oxide rhm oxide (Mg,Fe2+,Ti4+,Mn)2O3

pyrophanite — MnTiO3whitlockite wt Ca3(PO4)2troilite — FeSoldhamite — CaSosbornite — TiNgraphite — Ccohenite — Fe3C

Suppressed:cordierite — Mg2Al4Si5O18sapphirine — Mg4Al8Si2O20

Formulae are restricted to solid solution ranges present in calculations (cf. Ebel andGrossman, 2000). Ferric iron (Fe3+), although present in some solution models (spinel,Ca-px, rhm-ox), is insignificant in all calculated results shown here.


densate assemblages continually adjust so that the chemi-cal potential energy of the system is minimized. Feldsparis nearly pure anorthite. Textures in CAIs can be interpretedto show that anorthite was thermodynamically stable athigher temperatures than olivine and other phases, incon-sistent with calculated phase diagrams. MacPherson et al.(2004) discussed this phenomenon in the context of calcula-tions showing anorthite condenses at a higher T than forster-ite below Ptot ~ 10–4 bar (their Fig. 2), with dramatic effect(their Fig. 3). Calcium-pyroxene is stable in all these assem-blages. For the calculation by MacPherson et al. (2004) topredict the correct phase relations, the endmember pyroxeneenergies of Sack and Ghiorso (1994) must be innaccurate,but must be fortuitously corrected by MacPherson et al.(2004) ignoring the mixing properties included in the pyrox-ene model of Sack and Ghiorso (1994) (see section 3.1.2).Results of a calculation using the MELTS implementationof that model (Plate 8) illustrate that a narrow high-T anor-thite stability field does exist at very low Ptot < ~10–6.8. Iffeldspar (anorthite) were to form in this T-P range, then itmight survive metastably, relative to other phases, in a cool-ing system. Other arguments for anorthite stability have beendiscussed by Weisberg et al. (2005).

3.1.2. Comparison with other results. Several recentcalculations of equilibrium condensation are compared inFig. 1. Temperatures of mineral phase appearance and dis-

appearance are shown for three specific Ptot (bar) publishedas tables by Wood and Hashimoto (1993) and Petaev andWood (1998b), who did not include Ti or noble gases; Yo-neda and Grossman (1995), who included Ti and He butnot Ne or Ar; Petaev and Wood (2000), with Ti but no noblegases; Lodders (2003) who included the entire periodictable, but did not publish disappearance temperatures ofphases; and Ebel and Grossman (2000), whose methodswere the same as this work. Elemental abundances are fromAnders and Grevesse (1989) in all cases except for Lodders(2003). Inclusion or absence of noble (inert) gases slightlychanges the effective Ptot in the calculation. The absenceof Ti strongly affects phase stability, particularly by prevent-ing perovskite formation. There are many subtle compari-sons that could be made using these results; however, it istheir overall similarity, particularly for the major phasesfound in chondrites, that is striking.

All three groups used different data for the chemicalpotential energy (Gibbs free energy) of endmember min-eral phases, with varying degrees of documentation. Dif-ferences between Yoneda and Grossman (1995) and earlierwork are detailed in that paper, and differences between thatwork and Ebel and Grossman (2000), and by extension thepresent work, are explained in detail in the 2000 paper. Inparticular, the subtle equilibria among the Ca-aluminates(CA1, hib, grs) among the papers by Grossman’s group have

Fig. 1. Comparison of published results for vapor of solar composition (see section 3.1.2). Mineral abbreviations are t3 = Ti3O5, t4 =Ti4O7, C4T3 = Ca4Ti3O10, C3T2 = Ca3Ti2O7, sp = Al-spinel, cpx = Ca-pyroxene, and as listed in Table 1.


all been documented to result from choices of basic datamade for internal consistency with liquid solution models(Ebel and Grossman, 2000). The other major differencebetween Ebel and Grossman (2000), this work, and that ofPetaev and Wood (2000) appears to result from the formers’use of the complete MELTS (Sack and Ghiorso, 1994) cal-culation engine for Ca-pyroxene. Petaev and Wood (1998a,b,2000) use endmember data from, e.g., Sack and Ghiorso(1989, 1994), but they used ideal mineral-solution modelsfor the mixing properties of mineral solid solutions betweenthose endmembers (Petaev and Wood, 2000). Lodders (2003)did not consider solid solutions, so, for example, her “melil-ite” is pure gehlenite. For purposes of parameterizing con-densation for astrophysical calculations, all these results areadequate, and that of Lodders (2003) is preferred for itscomplete coverage of all the (astrophysical) “metals” (seesection 5.1). The work of Ebel and Grossman (2000), andthe present calculations, are most consistent with modelsof liquid solutions at conditions where the latter are thermo-dynamically stable, and include full implementation of theinternally consistent MELTS models for crystalline solu-tions that coexist with mafic (Mg-Fe-rich multicomponentsilicate) liquids.

3.2. Equilibria in Carbon-enriched Systems

Reduced phases are common constituents of enstatitechondrites (e.g., CaS, MgS, etc.) (Keil, 1968, 1989; Brearleyand Jones, 1998). Graphite, SiC, and TiC are commonpresolar grains (Meyer and Zinner, 2006). Both hydrous andanhydrous interplanetary dust particles (IDPs) are suffusedby C-rich intergranular material (Flynn et al., 2003), andCI chondrites contain up to 5 wt% C (Lodders and Osborne,1999). A diversity of carbonaceous material was abundantlypresent in the protoplanetary disk (Kerridge, 1999), so ex-ploration of mineral equilibria in hot, C-enriched systemsof otherwise solar composition has been an active area ofresearch (Larimer, 1975; Larimer and Bartholomay, 1979;Wood and Hashimoto, 1993; Sharp and Wasserburg, 1995;Lodders and Fegley, 1993, 1998).

Plate 9a illustrates stability relations among Ti-bearingphases, with other selected phases, shown in a narrow rangeof C/O where equilibrium chemistry changes dramatically(cf. Lodders and Fegley, 1997, their Fig. 3). At C/O < 0.85,equilibria are grossly similar to C/O ~ 0.43 (solar). OnlyTi-bearing phases are listed in most fields, while phaseboundaries of Ti-free phases x upon cooling at constant C/Oare labeled “+x.” The calculations were done using the dataand methods of Ebel and Grossman (2000). As the C/O ra-tio approaches unity, reduced phases become stable (e.g.,CaS, TiN, TiC). At C/O > 1, carbides and graphite are stableat the highest temperatures, and graphite condenses at pro-gressively higher T as C/O increases (Plate 9b). Oxides(e.g., Mg-olivine, spinel) are also stable at high C/O, be-cause condensation of graphite liberates O from gaseous CO.Metal becomes much more Ni-, Si-, and Co-rich than un-der oxidizing conditions. Intermetallic Fe-Si alloys are nottreated rigorously in the calculation, but information on these

compounds (e.g., FeSi, FeSi2) does exist (e.g., Meco andNapolitano, 2005). Unfortunately, while some data exist onbinary solutions, data is sparse regarding the thermochemi-cal behavior of more complex reduced solid solutions [e.g.,(Ti, Si, Zr)C, (Ti, Al, W)N, (Ca,Fe,Mg,Mn)S].

3.3. Equilibria in Dust-enriched Systems

Some mixture of dust grains is expected to accumulateat the midplane of the protoplanetary disk, and this dust maybe the precursor material for chondrule and/or CAI forma-tion. Ebel and Grossman (2000) investigated enrichment ofthe solar composition in a dust approximating the compo-sition of the meteorite Orgueil (Anders and Grevesse, 1989).Chondritic dust is a logical assumption, given the chondriticabundances observed in bulk protoplanetary material. Vari-ous other kinds of dust can be supposed, for example, aC-rich dust similar in composition to unequilibrated, an-hydrous, interstellar organic- and presolar-silicate-bearingcluster IDPs (Ebel and Alexander, 2005). Local vaporizationof micrometer-sized dust during rapid heating events (e.g.,Desch and Connolly, 2002; Joung et al., 2004) might affectchondrule composition by suppressing evaporation (Galyet al., 2000; Alexander et al., 2000). Vaporized dust wouldpromote preaccretionary metasomatic alteration, particularlyaffecting chondrule mesostasis (J. Grossman et al., 2002),or forming refractory alkali-bearing minerals in CAIs (e.g.,sodalite) (Allen et al., 1978; McGuire and Hashimoto, 1989;Krot et al., 1995; Nagahara, 1997).

Plate 10 illustrates the assemblages of solid and liquidphases that are calculated to be thermodynamically stablerelative to vapor, at fixed total pressure, Ptot = 10–3 bar, asfunctions of temperature (K) and enrichment in chondriticdust (cf. Ebel and Grossman, 2000). The oxides becomethermodynamically stable at progressively higher tempera-tures with increasing dust enrichment, leading to the sta-bility of liquids, and substantial FeO dissolved in silicates(Ebel and Grossman, 2000, their Fig. 8). Detailed resultssuch as calculated oxygen fugacity, FeO content of silicates,composition of metal alloy, and melilite composition arepresented in Ebel and Grossman (2000) for dust enrichmentincrements of 100×. Cordierite and sapphirine are calcu-lated to be stable below 1330 K, at dust enrichments <20×,but they are entirely omitted from this calculation for rea-sons detailed above. Calculations to even higher dust en-richments, essentially for a pure chondritic dust, were pre-sented by Ebel (2001).

4. METEORITIC EVIDENCEFOR CONDENSATION

4.1. Volatility-related DifferencesBetween Chondrites

Bulk compositions of chondrites are reviewed in detailby Hutchison (2004), who offers a somewhat strained di-chotomy of causal models for differences between them (hisTable 7.1). He concludes that “the chemical compositions


of the classes and groups of chondrites were established be-fore chondrule formation. Elemental fractionation correlateswith volatility . . . ,” when CI chondrites are considered to bethe most primitive, basic composition, due to their closestequivalence to the composition observed in the solar photo-sphere (Hutchison, 2004, p. 188). Regarding the constitu-ents of chondrites, Chiang (2002) characterizes chondrule(and CAI) formation as “a zeroth order” unsolved problem.Hutchison (2004, p. 192) considers the problem “even moreintractable and emotive than identifying the mechanisms forfractionating CI chondrite material to make the chondritegroups.” Chondrite compositions are not simply additivecombinations of Mg-Si chondrules, metal, and Ca-,Al-richinclusions. Instead, some complementarity must be invokedin which chondritic material was fractionated, based on rela-tive volatilities of elements, and then chondrules, etc.,formed from these fractionated batches (Hutchison, 2004,p. 193; Palme, 2001).

One approach to deciphering the elemental differencesamong the chondrites, and comparing them to planetarybodies, is to assume that volatile elements were added asdiscrete components. An obvious first choice is water ice(H2O). Figure 2a illustrates the abundances of selected ele-ments [atomic fraction of total; calculated from data of Was-son and Kallemeyn (1988); cf. Hutchison (2004)], with allH and O = 0.5 × H removed. The relative abundances of C

and S are still very high in CI and CM chondrites, relativeto the other classes (cf. Weisberg et al., 2006), with com-plementary depletion in Si, Mg, and Fe. Relatively volatilealkalies, and Se and Ga, are enriched in the same classes.Large variations in Fe are seen in the enstatite chondrites,particularly EH, and these are reflected in siderophile Co,Ga, and P, and chalcophile Se. These data suggest that Fealloy fractionation, perhaps even prior to chondrule forma-tion, contributed to the differences between these classes.

Figure 2b shows selected element abundances, recalcu-lated after subtraction of all C as pure C (consistent withstudies of interplanetary dust), and all S as SO2, which maybe less valid because it is not clear how important FeS wasas a chondrite precursor. This recalculation removes mostbias in illustrating the enrichment of CV and CO chondritesin highly refractory Al, Ca, Ti, Sc, and Zr. This is the ma-jor volatility-related fractionation seen in carbonaceouschondrites, and extends to other highly-refractory elementsnot shown here. The variation in alkalies (Na, K) is alsolikely to be related to their volatility. Variation in the sidero-phile elements (Fe, Co, P) is most pronounced among theordinary (H, L, LL) and enstatite (EH, EL) chondrites. Thecause of abundance variations of the siderophile elementsamong chondrites is not clear to this author. Loss (or gain)of metal grains, carrying siderophile elements in chondriticrelative abundances, has been hypothesized, but no cause

Fig. 2. Volatility-related elemental fractionation among chondrite groups, for selected elements with different cosmochemical affini-ties. (a) All H and O = 0.5*H subtracted. (b) All C and S (as SO2) subtracted.


is clearly established. More volatile chalcophile elements(“S-loving,” e.g., Se, Sb) would go along with these metalgrains, if they were condensed with them. Alternatively,some fraction of the chalcophile component, and also ofsimilarly volatile elements up to the temperatures of sta-bility of solids containing alkalies, was added to the chon-dritic components (chondrules, CAIs, metal grains, matrix)before (Allen et al., 1978) or during the components’ accre-tion into meteorite parent bodies.

4.2. Meteorite Components

A wide variety of inclusions and matrix grains is foundin meteorites, comprehensively reviewed by Brearley andJones (1998). Many have been hypothesized to be conden-sates, or to have equilibrated with vapor at high T in theprotoplanetary disk or nebula. These include, but are notlimited to, (1) “fluffy” type A (FTA) inclusions (MacPher-son et al., 1984; Beckett, 1986; but cf. MacPherson, 2003),spinel-pyroxene aggregates (Kornacki and Fegley, 1984;MacPherson et al., 1983), hibonite-bearing objects (Mac-Pherson et al., 1983; Hinton et al., 1988; Ireland et al.,1991; Russell et al., 1998; Simon et al., 1998, 2002; Mac-Pherson, 2003), and other highly refractory inclusions(Bischoff et al., 1985); (2) CAIs and chondrules (Wood,1963; Grossman and Clark, 1973; Wänke et al., 1974; Beck-ett and Grossman, 1988; Boss, 1996; Lin and Kimura, 2000;Scott and Krot, 2001; Kurat et al., 2002; Lin et al., 2003),particularly those with unfractionated REE abundance pat-terns (Russell et al., 1998); (3) minerals deposited in voidsin type B CAIs (Allen et al., 1978); (4) amoeboid olivineaggregates (Grossman and Steele, 1975; Komatsu et al.,2001; Aléon et al., 2002; Krot et al., 2004a; Weisberg et al.,2005); (5) metal grains in CB and CH chondrites (Meibomet al., 2001; Petaev et al., 2001, 2003; Campbell et al.,2001), and metal in CR chondrules (Connolly et al., 2001);(7) PGE nuggets (El Goresy et al., 1979; Palme and Wlotzka,1976) or opaque assemblages [a.k.a.-Fremdlinge (Sylvesteret al., 1990)] in CAIs; (8) relict hibonite (El Goresy et al.,1984) and fassaite (Kuehner et al., 1989; Lin and Kimura,2000) in CAIs and relict olivine (with included pockets ofsilicate melt) in chondrules and matrix (Olsen and Gross-man, 1978; Steele, 1986, 1995; Weinbruch et al., 2000; Packet al., 2004, 2005); (9) fine-grained components in matrixand inclusion rims (Wood, 1963; Wark and Lovering, 1977;Huss et al., 1981; Kornacki and Wood, 1984; Brearley,1993; Greshake, 1997; Ruzicka, 1997; Bischoff, 1998; Warkand Boynton, 2001; Zolensky et al., 2003); (10) xenolithsin Allende (Kurat et al., 1989); and (11) FeO-rich matrixolivine (Weisberg et al., 1997; Weisberg and Prinz, 1998).Some fraction of IDPs, probably sourced in comets, may becomposed almost entirely of condensates (Rietmeijer, 1998).

There is intense debate about what the extinct radioiso-topic systematics (MacPherson et al., 1995; Russell et al.,1998, 2006; McKeegan et al., 2000; Guan et al., 2000), O-isotopic signatures (McKeegan et al., 1998; Young and Rus-sell, 1998; Krot et al., 2002; Young et al., 2002; Clayton,

2004), and refractory mineralogies (Grossman, 1975; Simonet al., 1997, 1998, 2002; Russell et al., 1998) of CAIs im-ply about their formation histories, as reviewed by Mac-Pherson (2003) and in this volume. Fractional condensation,condensation followed by gas-phase metasomatism, andgas-solid equilibrium interrupted by melting events all seemto have affected the most refractory inclusions (e.g., Stolperand Paque, 1986). For example, condensation and aggrega-tion of solids to make fluffy type A CAIs, followed by reac-tion with vapor in the Ca-pyroxene stability field, followedby melting, may produce type B CAIs [e.g., Beckett (1986);perhaps at in Plate 7]. Evaporation of many type B CAIsis evident in their heavy isotope enrichment (Clayton et al.,1988), and the effect of evaporation on these objects is re-ceiving much attention (e.g., Nagahara and Ozawa, 2000;Galy et al., 2000; L. Grossman et al., 2002; Richter et al.,2002; Davis, 2003; Alexander, 2004). The precursor dustaggregates of many melted CAIs and chondrules are highlylikely to correspond in bulk composition to some assem-blages predicted in Plates 7 or 10. Predictions of other in-clusion compositions (e.g., radiating pyroxene chondrules)require very extraordinary conditions (Ebel et al., 2003).

Chondrules and igneous CAIs can be thought of as partof a continuum including Al-rich objects (Ebel and Gross-man, 2000, their Figs. 16 and 17; MacPherson, 2003; Mac-Pherson and Huss, 2005). Principal component analyses(Grossman and Wasson, 1983) and other evidence (Bischoffand Keil, 1984; Weisberg and Prinz, 1996) indicate theseinclusions formed by rapid melting of mixtures of precur-sor components. The precursors included refractory, Ca-,Al-rich material; less-refractory Mg-,Si-rich material; metalalloy and/or metal sulfide; and a more-volatile, Na- and Kbearing component (Grossman, 1996). Some CAIs may beartrace-element signatures that were established during stellarcondensation of their precursor grains (Ireland, 1990). Thesizes and relative proportions of inferred precursors werehighly variable, and some may be preserved as relict grains,for example, olivine (e.g., Steele, 1986; Jones, 1996; Packet al., 2005) and spinel (e.g., Misawa and Fujita, 1994;Maruyama and Yurimoto, 2003) in chondrules (cf. Misawaand Nakamura, 1996); perovskite in CAIs (e.g., Stolper,1982; Beckett, 1986). From a cursory inspection of Plates 7or 10, these precursor components are consistent with pro-gressive, volatility-controlled fractionation. The very exist-ence of CAIs, chondrules, and more volatile-rich matrixdemonstrates that such a fractionation process isolated theseobjects from thermochemical interaction in some locationsprior to their accretion into chondrites.

Disequilibrium processes are implicated in the formationof all the meteoritic material listed above. Chemical zon-ing is frequently observed in the crystals formed from meltin igneous objects. Some chondrules contain heterogene-ities in alkaline element contents and silicate mineral zoningthat may have resulted from gas-melt interactions (contin-ued condensation) during cooling (Matsunami et al., 1993;Tissandier et al., 2002; Krot et al., 2004a,b; Alexander andGrossman, 2005). Matrix assemblages of amorphous + crys-


talline silicates have been attributed both to disequilibriumcondensation (amorphous) followed by crystallization duringannealing (e.g., Brearley, 1993), or to equilibrium condensa-tion (crystalline) followed by amorphitization due to radia-tion damage (Zolensky et al., 2003). Fractional evaporationmay result in PGE-rich nuggets (Cameron and Fegley, 1982),and is certainly important in forming some CAIs (Davis,2003). Partial recondensation has been invoked in severalcontexts, for example, to explain compositions of rims onCAIs (Wark and Boynton, 2001).

4.3. Refractory Aluminum-Calcium-Silicon-Magnesium Phases

4.3.1. Calcium-aluminates. In most cosmochemicallyplausible protoplanetary chemical systems with C/O < 1,where liquid is not thermodynamically stable, corundum(Al2O3) is the highest-T solid to condense (Plates 7, 9a, and10; Fig. 1). Nearly pure corundum, enclosed in hibonite,with perovskite or grossite, has been reported in five inclu-sions (Bar-Matthews et al., 1982; Fahey, 1988; Krot et al.,2001). At least one (Simon et al., 2002) is convincingly notmelted, nor formed by reactions among less-refractory com-ponents, nor formed by evaporation (Floss et al., 1998). Thegrossite, perovskite, and spinel (MgAl2O4) found with hi-bonite in the most refractory CAIs are nearly pure phases(Table 1) (e.g., Weber and Bischoff, 1994; Simon et al., 1994;Brearley and Jones, 1998; Aléon et al., 2002). Calcium-monoaluminate has been reported in exactly one occurrence,with grossite, perovskite, and melilite (Ivanova et al., 2002).These assemblages are consistent with predictions in Plate 7for fractional condensation at high T and low Ptot, and atsmall dust enrichments (Plate 10).

Hibonite is calculated to condense after corundum in theabsence of liquid in systems with C/O < 1. Hibonites inCAIs can contain up to 6 wt% TiO2 + Ti2O3 (MacPhersonand Grossman, 1984; Brearley and Jones, 1998; Aléon etal., 2002). The Ti+3/Ti+4 ratio in hibonite is a sensitive in-dicator of oxygen fugacity (Ihinger and Stolper, 1986; Beck-ett et al., 1988). Spherules with nearly pure hibonite, sur-rounded by spinel, with or without perovskite, are rare com-ponents of several meteorite types that have been vigorouslyinvestigated (MacPherson et al., 1983; Hinton et al., 1988;Ireland et al., 1991; Floss et al., 1998; Simon et al., 2002).Textures of some inclusions [e.g., SH-6 of MacPherson etal. (1984)] provide compelling evidence of vapor-solid con-densation of euhedral hibonite plates, and subsequent reac-tion with vapor to directly form spinel. Beckett and Stolper(1994) argued, based on experimental results, that hibonitesin the core regions of melted Allende type A CAIs are sur-viving precursor grains.

4.3.2. Calcium-,aluminum-silicates. Melilite and Ca-rich pyroxene are, with spinel, the most abundant constitu-ent minerals of CAIs that are found in all chondrite classesexcept CI (Brearley and Jones, 1998; Fagan et al., 2000;MacPherson, 2003; Beckett et al., 2006). They sometimescontain measurable Sc and Zr (El Goresy et al., 2002; Simon

et al., 1991, 1996), and are highly depleted in more volatileelements (Na, Fe). Zoning in melilite crystals can be diag-nostic of their origin, whether they crystallized from a closed-system melt (igneous origin), a cooling melt in chemicalequilibrium with cooling vapor (metasomatic igneous), ordirectly from cooling vapor either fractionally or in equilib-rium (condensation senso stricto). Anorthite appears to haveformed by a vapor-solid reaction in many CAIs.

The least-melted CAIs record complex processes in thetextural relationships among the mineral phases. These tex-tures are disequilibrium phenomena that record sequential,incomplete, and partial equilibration of minerals with sur-rounding vapor. MacPherson (2003) and Beckett et al. (2006)have reviewed Wark-Lovering rim mineralogy and reversezoning of melilite in CAIs. An unresolved problem is theenclosure of spinel in melilite in most type A CAIs, becausespinel is calculated to form at lower T than melilite in mostconditions (Plates 7–10; Fig. 1). Beckett and Stolper (1994)argued that spinel growth on a hibonite substrate would bekinetically favored (over melilite growth) based on theircrystallochemical similarities. Alternatively, Beckett (1986)suggested that removal of hibonite-bearing objects rich inAl and the most refractory REE would both suppress melil-ite condensation relative to spinel, and also explain Group IIREE patterns.

In the condensation calculations shown here, the Al-,Ti-rich pyroxenes formerly known as “fassaite” (now, sub-silicic titanoan aluminian pyroxene) become stable at higherT than diopside (CaMgSi2O6), consistent with the experi-ments by Stolper (1982). The calculated compositions ofthose fassaites cannot be accurate, however, given the lackof Ti+3 in the model pyroxene. Although Ti+4 does notreadily enter tetrahedral sites in silicates, the behavior ofthe reduced species Ti+3 is relatively unknown, and couldhave significant effects on fassaite stability relative to otherphases. Yoneda and Grossman (1995) modified the esti-mates of pyroxene thermodynamic properties by Beckett(1986), and assumed ideal solution, to simulate condensa-tion of fassaite from solar and dust-enriched vapors at vari-ous total pressures (Ptot) below 1 bar. They condensed fas-saite at slightly lower temperature than melilite, but theirpredicted compositions (their Fig. 9) correspond poorly toobserved CAI fassaites (e.g., Beckett, 1986, Table 6; Simonet al., 1998). Scandium may also stabilize pyroxenes at highT. The thermodynamic properties of refractory Ca-,Al-,Ti-,Sc-pyroxenes remain mysterious. Sequential, incompleteequilibration of CAI pyroxenes with surrounding vapor isindicated by their chemical zoning (Brearley and Jones,1998), particularly in CAI rims. Texturally late FeO-enrich-ment probably results from aqueous alteration of rim pyrox-enes on chondrite parent asteroids.

4.3.3. Rare earth elements. Hibonite is the mineral sta-ble at the highest temperatures that incorporates significantREE (MacPherson and Davis, 1994; Ireland and Fegley,2000; Simon et al., 2002; Lodders, 2003). Rare earth ele-ment enrichments from 5 to 100×, and 0.6 to 5×, CI chon-dritic abundances are seen, respectively, in CAIs (Russell et


al., 1998) and in rapidly quenched chondrules (Engler et al.,2003) with unfractionated REE patterns. These objects mayretain the full complement of refractory lithophile REEscondensed directly into their precursors. Other CAIs andchondrules have patterns depleted in the more refractoryREE (Group II pattern) (cf. Mason and Taylor, 1982). Thesedepletions have been interpreted to result from the earliercondensation and removal of an ultrarefractory componentthat primarily retained the more-refractory REEs (Boynton,1975, 1978; Simon et al., 1994; Ireland and Fegley, 2000).Their volatility-related REE abundances, other isotopic con-straints, and high melting temperatures have been seen asevidence for CAI and chondrule origins as condensates nearthe Sun or in the Sun’s photosphere, and subsequent trans-port outward by stellar winds (Shu et al., 2001; Ireland andFegley, 2000). This idea resonates with the reasoning, be-fore any knowledge of REEs, of Sorby (1877), who arguedthat “some at least of the constituent particles of meteor-ites were originally detached glassy globules, like drops offiery rain.”

4.4. Metal Alloy and Ferromagnesian Silicates

4.4.1. Metal and siderophile elements. Metallic Fe-Nialloy is found as subgrains in presolar rocks (Bernatowiczet al., 1999) and is common in chondritic meteorites. Thechemical state of Fe (metal, sulfide, oxide) in chondrites,and the relative abundance of Fe among H, L, and LL ordi-nary chondrites, may result from fractionation of metals andS caused by their relative volatilities or succeptibility to oxi-dation and reduction in different regions of the protoplan-etary disk. Efforts to trace these processes are focussed onthe behavior of trace elements (siderophile) that dissolvein Fe (e.g., Blum et al., 1989). Some of the platinum-groupelements (PGE) are extremely refractory (Mo, Ru, Os, W,Re, Ir, and Pt), others less so (Fe, Ni, Pd, Co, Rh, Au, Cu)(Palme and Wlotzka, 1976; Humayun et al., 2002). The re-dox behavior of the siderophiles varies as well. Assemblagesof PGE-rich grains in CAIs have chondritic (solar) abun-dances of metals, although individual nuggets are highlyheterogeneous (MacPherson, 2003).

Zoned metal grains in some CB and CH chondrites havecore-to-rim gradients in composition that are correlated tothe relative volatilities of the metals. Campbell et al. (2001)could not reconcile zoning patterns with equilibrium frac-tional condensation. Yet these zoned grains have been in-terpreted by others to form by sequential equilibration withvapor, in calculations that account for diffusive processes(Meibom et al., 2001; Petaev et al., 2003). These modelsare capable of quantitatively matching many features of themetal grains, but they require a different set of parametersfor each grain (Petaev et al., 2001). Exactly how thesezoned metal grains formed is uncertain, pending better dif-fusion data on PGEs in metal.

Metal grains in chondrules have also been investigatedfor evidence of interaction with vapor. Recondensation isproposed to explain metal grains rimming CR chondrules,

and enriched in more volatile siderophile elements: InitiallyFeS- and FeO-bearing chondrules are heated and partiallyevaporate; crystals coarsen; metal is reduced and forms alloygrains, while volatile-enriched metal vapor recondenses asrims (Kong and Palme, 1999; Zanda et al., 2002). Alterna-tively, reduction occurs by equilibration with either a reduc-ing gas, or C present with the precursors (Huang et al., 1996;Hewins et al., 1997). Only a few weight percent C are nec-essary to reduce most of the fayalite in typical chondrules(Connolly et al., 1994). Connolly et al. (2001) concludedfrom experimental work (cited therein) that vapor is a lesslikely reductant than included C (cf. Hanon et al., 1998).Lauretta et al. (2001) came to a similar conclusion, and esti-mated 4.6 wt% Si in chondrule metal formed by this pro-cess in ordinary chondrites, far higher than would condensein an oxidizing (solar or dust-enriched) environment (Gross-man et al., 1979; Ebel and Grossman, 2000). They wentfurther, and assumed volatile (O, S, and Na) addition aftermetal formation, through interaction with surrounding va-por at lower T, and used commercially available code [HSC(Eriksson and Hack, 1990)] to predict the corrosion of Si-,P-, Ni-bearing metal to silica (SiO2), troilite (FeS), and otherfine-grained phases they observed in SEM images. One dif-ficulty with the in situ C-reduction hypothesis is the absenceof C from metal in carbonaceous chondrites (Mostefaouiet al., 2000).

4.4.2. Magnesium-(iron)-silicates. The elements Fe,Mg, and Si are ~10× more abundant than the more refrac-tory Al and Ca. Olivine (Mg-orthosilicate, Table 1) has beencalled “astrophysical silicate,” because the olivine speciesforsterite (Mg2SiO4) is the most refractory silicate to con-dense from a solar gas in quantity. For example, at Ptot =10–3 bar, ~0.0027% of all atoms are condensed at 1444 Kwhen forsterite appears, and ~0.0150% are condensed asolivine, out of ~0.0165% total, at 1370 K. This small T (or,alternatively, Ptot) interval coincides with the transition fromrefractory inclusion (CAI) assemblages to chondrule min-eral assemblages. It is unlikely that most meteoritic inclu-sions or their precursors passed through this interval in asmooth, monotonic way; they probably experienced fluc-tuations in T and Ptot.

Olivine is the most abundant silicate in most chondrites;however, there is only controversial evidence that any oli-vine is a primary condensate, or reached equilibrium withvapor (McSween, 1977; Olsen and Grossman, 1978; Palmeand Fegley, 1990; Steele, 1986, 1995; Weisberg et al., 1997;Weisberg and Prinz, 1996, 1998; Weinbruch et al., 2000;Pack et al., 2004). The FeO and Na2O content of many me-teoritic silicates has been altered during secondary process-ing on parent bodies, obscuring the signatures of preaccre-tionary processes (Bischoff, 1998; Sears and Akridge, 1998;Krot et al., 2000; Brearley, 2003). If all Fe in a gas of solarcomposition (Mg/Si ~1.07) existed as metal, orthopyroxene(enstatite, MgSiO3) would dominate the silicate assemblage,as it does in enstatite chondrites. In condensation from so-lar gas, FeO-bearing silicates only form by reaction of metaland metal sulfide with Mg-silicates and vapor at very low


temperatures, where diffusion is slow. Alternatively, FeO-bearing chondrules may have formed from flash-meltedFeO-bearing precursors that crystallized at low temperaturesor in an oxidizing environment, without losing FeO by evap-oration during melting. Negligible heavy Fe-isotopic en-richment is observed in chondrule silicates (Zhu et al., 2001;Alexander and Wang, 2001; Mullane et al., 2003). Flashmelting would then have had to occur in a vapor enrichedin Fe (Galy et al., 2000; Alexander, 2001; Ebel, 2005). Simi-lar issues are involved with the Na content of chondrulesand CAIs (e.g., Sears et al., 1996).

One way to increase the FeO content of silicates whenthey first become chemically stable is for the surroundingvapor to be enriched in O. Ebel and Grossman (2000, theirFig. 8) showed that above 1200 K, systems enriched inchondritic vapor yield ferromagnesian silicates with mo-lar FeO/(FeO + MgO) ratios of 0.1–0.4, and also stabilizechondrule liquids against evaporation (Plate 10). Alterna-tively, enrichment of vapor in H2O ice can stabilize FeO insilicates at high temperature (Krot et al., 2000, their Fig. 6).Mechanisms capable of melting chondrule precursors [shockwaves, Desch and Connolly (2002); current sheets, Jounget al. (2004)] would simultaneously vaporize small silicatedust grains, providing a local dust-enriched region duringchondrule cooling.

4.5. Carbides, Sulfides, and Phosphides

Presolar grains have survived ejection from AGB starsor novae, interstellar processing (Bernatowicz et al., 2006;Nuth et al., 2006), presolar cloud collapse (Boss and Gos-wami, 2006) heating and irradiation in the early solar nebula(Connolly et al., 2006; Chaussidon and Gounelle, 2006;Chick and Cassen, 1997), accretion into chondrite parentbodies (Cuzzi and Weidenschilling, 2006; Weidenschillingand Cuzzi, 2006), followed by aqueous alteration (Brearley,2006), impacts (Bischoff et al., 2006), lithification, and ther-mal metamorphism on the parent bodies (Huss and Lewis,1995; Zinner, 1998; Mendybaev et al., 2002; Krot et al.,2006; Huss et al., 2006). Graphite, SiC, TiC, Fe-Ni alloy,spinel, corundum, and other presolar phases are all refractoryminerals predicted to condense from vapors with variableC/O ratio but solar proportions of other elements (Plate 9b)(Ebel, 2000). Isotopic constraints on grains formed in super-novae require mixing between different chemical zones ofsupernovae, if the grains condensed in systems approach-ing equilibrium (Travaglio et al., 1999; Ebel and Grossman,2001; Meyer and Zinner, 2006). Quantitatively addressingthe condensation of these rocky materials would appear torequire better models of zone mixing in supernova explo-sions, to reduce the universe of possible mixtures capable ofproducing the observed condensates.

Enstatite chondrites contain mixed phases in the FeS-MnS-MgS system (niningerite, alabandite), which may re-cord primary equilibrium with vapor (El Goresy et al., 1988;Crozaz and Lundberg, 1995; reviewed by Brearley andJones, 1998). Metal (Plate 9b) is Si-rich, and the Si content

of metal increases steadily as coexisting vapor becomesmore highly reducing, until the stability fields of Fe-Si in-termetallic compounds are reached at high C/O ratios of thebulk system. These compounds are not observed in mete-orites. Other common phases include oldhamite, nearly pureCaS; troilite, FeS; daubreelite, (Fe, Mn, Zn)Cr2S4; schrei-bersite, FeNi3P; and perryite, ~(Ni,Fe)2(Si,P). Other sulfideshave been discovered in enstatite chondrites, but their cos-mochemical significance is unknown (e.g., Nagahara, 1991).The role of vapor-solid equilibria in the origin of compo-nents of enstatite chondrites remains poorly constrained.

5. DISCUSSION AND CONCLUSIONS

5.1. The 50% Condensation Temperature

Wasson (1985, his Table G1) has compiled a table of“50% condensation temperatures” for the elements fromprevious calculations (e.g., Wai and Wasson, 1979; Lodders,2003). This single metric has been useful in categorizing theelements by their volatility in a gas of solar composition atfixed Ptot (e.g., Hobbs et al., 1993), but can be misleadingbecause elements condense over different T ranges (Ebel,2000). Lodders (2003) treated the entire periodic table in aself-consistent manner, to calculate 50% condensation tem-peratures at Ptot = 10–4 bar, using her assessment of the mostrecent elemental abundance data for a vapor of solar compo-sition (see section 3.1.2).

5.2. Contexts of Condensation andGas-Vapor Equilibrium

Incontrovertible evidence for direct condensation ofrocky meteoritic material from vapor to solid or liquidphases remains elusive, apart from micrometer- to sub-micrometer-sized presolar grains formed around other stars,probably in single outflow episodes. These grain sizes can-not be taken as exemplary of solar nebular processes. Ex-cept for some isotopic anomalies that may have resultedfrom local processes [e.g., O self-shielding (Navon andWasserburg, 1985; Clayton, 2004)], the initial gas and dustof the protoplanetary disk appear to have been thoroughlymixed (Palme, 2001). Most grains that may represent directvapor-solid condensates, even in unmelted IDPs, are isoto-pically solar at the spatial resolution of current instruments.It is not clear how this homogenization occurred, if the solarsystem was hot only inside ~3 AU, unless mixing in theaccretion shock was highly efficient. Perhaps the interstel-lar medium, the ultimate source of precursor solids, is alsomostly well-mixed, most grains are submicrometer-sized,and a “scoop” of them is essentially solar (Brearley, 1993).It is also possible that thin planar heating events, such ascurrent sheets and shock waves, driven by magnetorota-tional and gravitational instabilities, were commonplace indifferent regions of the protoplanetary disk well beyond3 AU. These forces would have driven repeated cycling ofmicrometer-sized solids through the vapor phase, building


up a supply of ever-larger condensate grains, and depletingregions of the disk in the same volatility-controlled patternsobserved in dense molecular clouds (Ebel, 2000). Result-ing larger dust and dust aggregates would be isotopicallyclose to solar if evaporating materials were unmelted. Bothshocks and current sheets would produce local T excursionsdecreasing with radial distance from the central star. Thisis one context for direct condensation in the early solarsystem. Future astronomical observations of disks at highspatial resolution, by coronography and/or interferometry,should reveal whether such fractionation exists and at whatradii from central stars. The precursors to chondrules andCAIs were probably similar to IDP components, isotopi-cally solar in most respects, and fractionated into Ca-,Al-,Ti-rich oxides; Mg-,Si-rich silicates; metal; and weaklybonded components rich in volatile elements.

Rietmeijer (1998) has developed a theory of “hierarchi-cal accretion” in explaining the textures and compositionsof IDPs. Meteoritic inclusions experienced many episodesof heating to high temperatures, so their textures would notreveal hierarchical accretion as clearly as do IDPs. But theparadigm may apply most evidently to more refractoryCAIs, and to AOAs, where sequential layers of minerals,mechanically accreted, were also subsequently changed bysequential metasomatic reactions with vapor. Many objectspreserve layers of minerals of different volatility, as if theypassed through regions rich in, and accreted rims of, dustthat had been condensed at a particular temperature, Ptot,and vapor composition (MacPherson et al., 1985). As theobjects themselves occasionally encountered more than onesuch heating event, dust would progressively sinter andacquire an igneous texture, becoming part of the chondruleor CAI, and also reacting with gas, for example, a gas withhigher PSiO than encountered previously. Hierarchical ac-cretion may be caught in the act, in concentrically zonedCAIs (e.g., Simon et al., 1994), or in chondrules with thicklayers of dusty rim material, and with concentric internalstructure. Partial or complete remelting of such objectswould sinter the rim or homogenize the entire object, evenas it accreted still more dusty material. This scenario re-quires a high dust-to-gas ratio, with heating events evapo-rating nearby fine dust particles so that vapor pressures ofO and condensable elements are locally increased aroundmelted chondrules. This would suppress evaporative enrich-ment in heavy isotopes, make liquids stable against evapo-ration, and increase the stable FeO content of silicates. Thiskind of accretion, resulting in chondrules and CAIs, wouldoccur in disk regions closer to the Sun, with higher densi-ties of dusty material.

Vapor-solid-liquid equilibria appear to have been ap-proached inefficiently, due to the rapid timescales of mostheating events, resulting in the abundant evidence of dis-equilibrium in the heterogeneous and zoned mineral grainsof so many meteoritic inclusions. It is also likely that ki-netic and surface effects are important in stabilizing particu-lar minerals relative to others, in direct gas-solid reactions(Beckett, 1986). Differences in thermochemical stability be-

tween these phases are small, so surface energy effectsbecome important at small grain sizes. Surface forces mayaffect macroscopic grain compositions, as they do in sector-zoned crystals. Displacive reactions of preexisting, more re-fractory phases (e.g., melilite) with vapor during coolingmight also be energetically favored, relative to reconstruc-tive reactions (i.e., adjusting a few vs. breaking many bonds).This may explain textures in unmelted objects, in which an-orthite appears to have formed at a higher T than olivine(e.g., Krot et al., 2002; Weisberg et al., 2005).

6. OUTLOOK

6.1. Observations of Meteorites

The equilibrium chemical behaviors of the abundant ele-ments (Si, Fe, Ni, Mg, Al, Ca, Ti) are well understood ex-cept in highly reduced systems. Attention has shifted to theless-abundant elements. We can expect increasing applica-tion of new, high-resolution analytical techniques to elemen-tal and isotopic abundances in particular components ofmeteorites, and correlation of these results with other evi-dence (e.g., Mullane et al., 2001; Young et al., 2002; Kehmet al., 2003; Friedrich et al., 2003; Dauphas et al., 2004;Johnston et al., 2004). New techniques of laser ablation ion-coupled plasma mass spectrometry (LA-ICPMS) enableinvestigation of ever-smaller spatial regions of metal grains(e.g., 30 µm × 15 µm deep) at very high mass resolution(Campbell and Humayun, 1999). The moderately volatileelements (e.g., Mn, Cu, Na, Se, Zn, Cd) are increasinglyaccessible to chemical and isotopic analysis in meteoriticmaterials. High compositional accuracy and fine spatialresolution of analyses of these and other trace elements willallow new constraints to be placed on the vapor-solid-liq-uid equilibria operative in the formation of chondritic com-ponents.

The search for extrasolar planets is driving astrophysi-cal observations of disks around nearby young stars that willyield images of increasingly higher spatial and spectralresolution. It will be possible to ascribe radial gradients inelemental abundances of disk gas to grain formation and/ordestruction. Better constraints on temperatures in evolvingdisks should also result from these observations. It is hopedthat these results will have direct relevance to the origin ofthe rocky material in chondritic meteorites.

6.2. Theory

Condensation calculations relevant to meteorites aregrounded in over a century of systematic experimental pe-trology, mineralogy, and basic research (e.g., Bowen, 1914;Ferguson and Buddington, 1920; Robie et al., 1978; Yoder,1979; Chase, 1998). Results of this difficult work, withmodern computational tools, provide the means to calibratemathematical models for the thermodynamic behavior ofminerals and melts (Charmichael and Eugster, 1987; Gei-ger, 2001). These fields are perhaps not as actively sup-


ported as they once were. The public availability of high-quality primary experimental data by metallurgists and ma-terials scientists appears to have declined since the 1970s.At the same time, the computer has enabled collation andevaluation of subsets of the mountain of existing data, re-sulting in open databases (e.g., Berman, 1988; Kuzmenkoet al., 1997) usually optimized for particular subsets of thecosmochemical universe [e.g., THERMOCALC for meta-morphic petrology (Holland and Powell, 1998)]. Proprietarydatabases [e.g., FactSage (Bale et al., 2002)] also exist, buttheir reliability is difficult to assess.

Strong backgrounds in thermodynamics and experimen-tal petrology are necessary for critical assessment of exist-ing data; for the building of optimized, internally consistentdatabases, both for equilibrium and kinetic approaches; forimprovement of solid- and liquid-solution models appli-cable to extraterrestrial rocky materials; and for informeduse of computational tools. Non-open-source, “black-box”software is increasingly available to perform equilibriumthermodynamic calculations with some degree of presumedrigor. These must be used with caution. Progress is mostlikely to result from the combination of kinetic constraintswith thermodynamic models, in open-sourced codes. Earlyand rigorous training of students in thermodynamics, iso-tope chemistry, and experimental petrology must be thefoundation for future progress in reading the solar system’searliest rocks.

6.3. Experiments

New techniques are being developed to directly probecondensation phenomena (e.g., Toppani and Libourel, 2003;Toppani et al., 2005). The Knudsen cell has, belatedly,begun to see more application in petrologically relevant ex-periments (e.g., Dohmen et al., 1998). The combination oflaser-heating devices and quadrupole mass spectrometersto measure gas speciation promises to allow direct investiga-tion of both condensation and evaporation. The parametersnecessary to model evaporative mass fractionation are beingdiscovered in the laboratory (Davis et al., 1990; Richter etal., 2002; Dauphas et al., 2004). Amorphous grains 20–30 nm in size condense via homogeneous nucleation fromhot gases quenched in short times (Nuth et al., 2002). Theirannealing to crystalline phases as a function of time andtemperature has been quantified with application to ob-served AGB outflows, and to make inferences about proto-planetary disk grain cycling (Brucato et al., 1999; Nuth etal., 2002). Other recent work at slightly longer timescaleshas resulted in partially or fully crystalline olivine con-densed from vapor (Tsukamoto et al., 2001). Even longertimescales are being explored, in heterogeneously nucleatedsystems (Toppani et al., 2004). Gas-grain reactions at lowertemperatures (<600 K) are also being explored (Llorca andCasanova, 1998). These kinds of experiments become mostrelevant to the processes recorded by objects in meteorites,when combined with kinetic models grounded in an under-

standing of equilibrium phase relations. We can expectsubstantial progress both in direct laboratory explorations,and their understanding using better models, by the nextedition of this volume.

Acknowledgments. This research has made use of NASA’sAstrophysics Data System Bibliographic Services. This work waspartially supported by the NASA Cosmochemistry program undergrant NAG5-12855.

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